Simultaneous p-Orderings and Equidistribution

Anna Szumowicz ()
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Anna Szumowicz: Mathematics and Astronomy, Caltech, The Division of Physics

A chapter in Algebraic, Number Theoretic, and Topological Aspects of Ring Theory, 2023, pp 427-442 from Springer

Abstract: Abstract Let D be a Dedekind domain. Roughly speaking, a simultaneous 𝔭 $$\mathfrak {p}$$ -ordering is a sequence of elements from D which is equidistributed modulo every power of every prime ideal in D as well as possible. Bhargava in (Journal für die reine und angewandte Mathematik 490 (1997), 101–128) asked which subsets of the Dedekind domains admit simultaneous 𝔭 $$\mathfrak {p}$$ -orderings. We give an overview on the progress in this problem. We also explain how it relates to the theory of integer-valued polynomials and list some open problems.

Date: 2023
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DOI: 10.1007/978-3-031-28847-0_22

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